Problem: Solve for $x$ and $y$ using elimination. ${-x-4y = -29}$ ${x+5y = 34}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-x-4y = -29}\thinspace$ to find $x$ ${-x - 4}{(5)}{= -29}$ $-x-20 = -29$ $-x-20{+20} = -29{+20}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 5}$ into $\thinspace {x+5y = 34}\thinspace$ and get the same answer for $x$ : ${x + 5}{(5)}{= 34}$ ${x = 9}$